Question

1. (2x + 8)° (3x + 17)°

Explanation:

Step1: Recognize linear pair sum

The two angles form a linear pair, so their sum is $180^\circ$.
$(2x + 8) + (3x + 17) = 180$

Step2: Combine like terms

Add the variable terms and constant terms.
$5x + 25 = 180$

Step3: Isolate variable term

Subtract 25 from both sides.
$5x = 180 - 25 = 155$

Step4: Solve for x

Divide both sides by 5.
$x = \frac{155}{5} = 31$

Step5: Calculate each angle

Substitute $x=31$ into each angle expression.
First angle: $2(31) + 8 = 62 + 8 = 70^\circ$
Second angle: $3(31) + 17 = 93 + 17 = 110^\circ$

Answer:

$x=31$, the two angles are $70^\circ$ and $110^\circ$